Question

В ат­трак­ци­о­не че­ло­век мас­сой 70 кг дви­жет­ся на те­леж­ке по рель­сам и со­вер­ша­ет «мерт­вую петлю» в вер­ти­каль­ной плос­ко­сти. С какой ско­ро­стью дви­жет­ся те­леж­ка в верх­ней точке кру­го­вой тра­ек­то­рии ра­ди­у­сом 5м, если в этой точке сила дав­ле­ния че­ло­ве­ка на си­де­ние те­леж­ки равна 700 Н? Уско­ре­ние сво­бод­но­го па­де­ния при­нять рав­ным

Answer 1

Дано:
m = 70 кг
R = 5 м
P = 700 Н
g = 10 м/с²

V - ?

Ускорение тележки:
a = V² / R

Вес человека в верхней точке траектории:
P = m*(g - a) или
P = m*(g - V² / 2)

Отсюда:
g - V² / R = P / m
V² / R = (g - P / m)
V² = R * (g - P/m)
V² = 5 * (10 - 700/70) = 5*(10 - 10) = 0

Ответ: V = 0 м/с

Answer 2

Calculation of the Speed of the Cart in the Upper Point of the Circular Path

To calculate the speed of the cart in the upper point of the circular path, we need to consider the forces acting on the person and the cart. In this case, the force of pressure exerted by the person on the seat of the cart is relevant.

Given: - Mass of the person = 70 kg - Radius of the circular path = 5 m - Force of pressure exerted by the person on the seat of the cart = 700 N

To find the speed of the cart in the upper point of the circular path, we can use the principle of conservation of mechanical energy. At the highest point of the circular path, the potential energy of the person is maximum, and the kinetic energy is zero.

The total mechanical energy at the highest point is the sum of the potential energy and the kinetic energy:

Total mechanical energy = Potential energy + Kinetic energy

At the highest point, the potential energy is equal to the gravitational potential energy:

Potential energy = mgh

where: - m is the mass of the person (70 kg) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the height from the ground to the highest point of the circular path (equal to the radius of the circular path, 5 m)

Substituting the values, we have:

Potential energy = (70 kg) * (9.8 m/s^2) * (5 m) = 3430 J

Since the kinetic energy is zero at the highest point, the total mechanical energy is equal to the potential energy:

Total mechanical energy = 3430 J

The total mechanical energy is also the sum of the kinetic energy and the potential energy:

Total mechanical energy = Kinetic energy + Potential energy

Since the kinetic energy is zero, we can rewrite the equation as:

3430 J = 0 J + Potential energy

Simplifying the equation, we find:

Potential energy = 3430 J

Now, we can calculate the speed of the cart in the upper point of the circular path using the formula for potential energy:

Potential energy = (1/2) * m * v^2

where: - m is the mass of the person (70 kg) - v is the speed of the cart in the upper point of the circular path

Rearranging the equation, we have:

v^2 = (2 * Potential energy) / m

Substituting the values, we get:

v^2 = (2 * 3430 J) / 70 kg

Calculating the value, we find:

v^2 ≈ 98.286 m^2/s^2

Taking the square root of both sides, we find:

v ≈ 9.914 m/s

Therefore, the speed of the cart in the upper point of the circular path is approximately 9.914 m/s.